Journal of East China Normal University(Natural Science) ›› 2021, Vol. 2021 ›› Issue (3): 8-16.doi: 10.3969/j.issn.1000-5641.2021.03.002

• Mathematics • Previous Articles     Next Articles

Modules and induced modules of 3-Lie algebra Aω δ

Ruipu BAI1,2(), Yue MA1,2   

  1. 1. College of Mathematics and Information Science, Hebei University, Baoding Hebei 071002, China
    2. Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, Baoding Hebei 071002, China
  • Received:2020-02-18 Online:2021-05-25 Published:2021-05-26


For the infinite dimensional simple 3-Lie algebra $A_{\omega}^{\delta}$ over a field $\mathbb F$ of characteristic zero, we construct two infinite dimensional intermediate series modules $(V, \rho_{\lambda, 0})=T_{\lambda, 0}$ and $(V, \rho_{\lambda, 1})=T_{\lambda, 1}$ of $A_{\omega}^{\delta}$ as well as a class of infinite dimensional modules $(V, \psi_{\lambda,\mu})$ of ad $(A_{\omega}^{\delta})$ , where $\lambda, \mu\in \mathbb F$ . The relation between 3-Lie algebra $A_{\omega}^{\delta}$ -modules and induced modules of ad $(A_{\omega}^{\delta})$ are discussed. It is shown that only two of infinite dimensional modules, namely $(V, \psi_{\lambda, 1})$ and $(V, \psi_{\lambda, 0})$ , are induced modules.

Key words: 3-Lie algebra-module, induced module, intermediate series module

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